Theorem necom 2498

Description: Commutation of inequality. (Contributed by NM, 14-May-1999.)

Assertion

Ref	Expression
necom	|- ( A =/= B <-> B =/= A )

Proof of Theorem necom

Step	Hyp	Ref	Expression
1		eqcom 2236	. 2 |- ( A = B <-> B = A )
2	1	necon3bii 2452	1 |- ( A =/= B <-> B =/= A )

Syntax hints:   <-> wb 105   =/= wne 2414

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 619  ax-in2 620  ax-5 1496  ax-gen 1498  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-cleq 2227  df-ne 2415

This theorem is referenced by:  necomi  2499  necomd  2500  difprsn1  3839  difprsn2  3840  diftpsn3  3841  fndmdifcom  5790  fvpr1  5894  fvpr2  5895  fvpr1g  5896  fvtp1g  5898  fvtp2g  5899  fvtp3g  5900  fvtp2  5902  fvtp3  5903  netap  7585  2omotaplemap  7588  zltlen  9678  nn0lt2  9681  qltlen  9994  fzofzim  10553  flqeqceilz  10708  isprm2lem  12843  prm2orodd  12853  tridceq  16982